This *is* a surprise. Mostly because KSA tends to lean on other countries in the region on not allowing such. It's not a surprise it would be Qatar that would take the first step at such.
Christian church rises in Arabia (al-Jazeera)
"Work has begun on the construction of Qatar's first purpose-built church in the desert outside Doha, the country's capital.
Although the country's native inhabitants are entirely Muslim - and are prohibited by law from converting to another faith - the new Catholic church will cater to the large number of Christian migrants who have come to the Arabia Gulf state in search of work.

Roman Catholics from all over the Arabian Peninsula - many of them migrant workers - are helping to pay for the $15m building, which is scheduled to open at the end of the year.
Overseeing the church is Paul Hinder, the Catholic Church's Bishop of Arabia. A Christian in the heart of the Muslim world, his diocese is the entire Arabian peninsular, encompassing six countries."